. Consider the following system. The spring is unstretched when y=yo, and gravity is included. The mass m slides with no friction on the guide in the radial direction. The circular frame has mass moment of inertia J about its center and rotates about the pivot O at its center. (i) How many DOF does this system have? Is it conservative or nonconservative, and why? (ii) Use Lagrange's equation(s) to find the equation(s) of motion of this system. (ii) Now, suppose that the circular frame rotates with a prescribed constant angular velocity w, so that the angle is known and equal to 8= wt. In that case, how many DOF does the system have? Derive the equation(s) of motion. g 1 6.D R m NG EST 2 e(t) J